Modeling water waves beyond perturbations

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Abstract

In this chapter, we illustrate the advantage of variational principles for modeling water waves from an elementary practical viewpoint. The method is based on a ‘relaxed’ variational principle, i.e., on a Lagrangian involving as many variables as possible, and imposing some suitable subordinate constraints. This approach allows the construction of approximations without necessarily relying on a small parameter. This is illustrated via simple examples, namely the Serre equations in shallow water, a generalization of the Klein–Gordon equation in deep water and how to unify these equations in arbitrary depth. The chapter ends with a discussion and caution on how this approach should be used in practice.

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Clamond, D., & Dutykh, D. (2016). Modeling water waves beyond perturbations. Lecture Notes in Physics, 908, 197–210. https://doi.org/10.1007/978-3-319-20690-5_7

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